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The size container will depend on the size of plant that you are starting with.
A 2 gallon nursery pot may be potted into a container such as a half whiskey barrel.
You will need to provide some extra winter protection for a potted burning bush. You can wrap it with insulation or move to a sheltered area such as a garage after it has gone dormant.

https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm

Full sun and well draining soil!
This article has more information.

https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm

The Lady Bugs were likely feeding on the bad insects.
Treat the plant with Neem Oil which is safe for people, pets and bees.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/beneficial-insects.htm

Locate the burning bush in well-draining soil, because it does not like soil that stays wet for long periods. Depending on the rain and fog level of the area, water the plant only when a dry spell occurs. Pour the water on the ground around the bush. Watering with a sprinkler doesn't soak the ground well enough. Let the ground dry out between watering. Normally the burning bush needs water once a week during the summer.

Mulching benefits the burning bush by keeping the roots cool and conserving water. Spread about an inch of organic mulch around the root zone. Organic mulch includes shredded newspaper, sawdust, dried grass clippings and dead leaves. These materials break down over time and slowly add natural nutrients to the soil.

Spider Mites and Scale are common on a Burning Bush and can cause leaf drop if the infestation is not kept in control.

https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm

These articles should help
https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-turning-brown.htm

https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/bugs-on-burning-bush-plants.htm

Burning bushes have lots of suckers. The are cousins to Nandinas. Cut them back very low to the grow to about 6 inches if you can. Spray them with equals parts of salt and water. That will kill the roots. If you can,t manage that since I don't know just how many you have you can torch them in the winter or pull them out with a farm jack. The latter is a pain but it will get rid of them.